Question

How do I find the least upper bound of a set?

Answer 1

Hint: Any non-empty set of real numbers with an upper bound must also have a least upper bound in real numbers, according to the least-upper-bound property.

Complete step-by-step answer:
Step 1: Find the upper bound of the set.
Any number that is equal to or greater than all the elements of the set.
For example: for the interval $[0,1]$ , $5$ can be an upper bound.
Step 2: The smallest number among the upper bound set of numbers is the least upper bound.
For example: for the interval $(5,7)$ , $7$ is the least upper bound.

Note: The least upper bound is not to be confused with the greatest lower bound.
Any non-empty set of real numbers with a lower bound must also have a greatest lower bound in real numbers, according to the greatest lower bound property.